Microscopic Treatment for the Degree of Freedom Beyond the S-D Model Space

A microscopic treatment of the collective degrees of freedom of nuclei beyond the S-D model space in interacting boson model is given.Following a similar line as in the case of defining the seniority particle operator,independent of the S degree of freedom in single j-shell,a modified S,D pairs and generalized OBT(operatorized Bogoliubov transformation)are introduced to separate both the S and D degrees of freedom from the rest in the model space of the nucleus spanned by a set of nucleon creation operators c†jm(j=j1,j2,...).